As noted by Florida Fan, the notched tail is clearly shown in this case. Indeed, this is the best example I've ever seen. The notched tail can be used to differentiate the L3 larvae of S. stercoralis with those of hookworm (the latter has a pointed tail).
BW in VT noted that the patient may have acquired infection years ago, and maintained infection via ongoing autoinfection. This is an important component of the S. stercoralis life cycle, as it allows for infection to persist for decades. Should the patient become immunocompromised, the ongoing infection can produce a hyperinfection state, leading to severe morbidity and possible death.
From Blaine: Silly stringy Strongyloides stercoralis stealthily slithers in sputum, spied by sensational Specialists.